Ant colony algorithm for driving variance reduction

techniques in Monte Carlo simulations

Salvador García-Pareja

Gloria Díaz-Londoño

Fabián Erazo

Francesc Salvat

Antonio M. Lallena

Introduction

The Monte Carlo simulation is a useful tool in the study of

radiation transport.

High degree of agreement with experimental

measurements.

Precision Simulation time

Variance reduction techniques can solve the problem.

Introduction

Variance reduction techniques:

•Russian Roulette, splitting, interaction forcing, etc.

•Statistical weight is assigned to every particle for keeping

the simulation unbiased.

•Used properly they can increase efficiency. Otherwise,

efficiency could even decrease.

How to use them properly?

Introduction

The algorithm has been developed studying different

situations regarding medical applications of ionizing

radiation.

We have chosen the PENELOPE Monte Carlo code for

the radiation transport simulations.

Aim of this work: To find an algorithm that permits the

application of these techniques optimizing the simulation

with a minimal intervention from the user.

Electron beams

Widely used in near-surface

treatments.

In the presence of heterogeneities

MC is the best choice of

calculation.

Essential a good characterization

of the beam.

Electron beams

Geometry of Mevatron

Siemens KDS acceleratorFilters

Window

Ionization chamber

Jaws

Phantom

Windowe- source

First Filter

Second Filter

Layer of gold

Layer of Kapton

Ionization Chamber

Electron beams

12 MeV electron beam PDD in a water phantom.

Typical simulation parameters. PC Pentium 4 (1.6 GHz).

Time to reach 2% uncertainty (k = 3): 220 h.

Electron beams

The problem

Most of that time is spent simulating

electrons that are absorbed by the jaws

(~ 80%).

Possible solutions for electrons:

•Russian Roulette: Reduce time but

increases variance.

•Splitting: Reduce variance but increases

simulation time.

Electron beams

The problem

Where to apply Russian roulette or splitting?

Test simulations Optimization

algorithms

Electron beams

Ant Colony Optimization Algorithms

Algorithms based on ant behavior:

•Ants look for food following a random walk.

•If they find food, then they come back to the nest

depositing pheromone.

•The other ants tend to follow the pheromone trail.

•The overall effect is an increased deposition of

pheromone on the optimal path between food and nest.

Electron beams

Nest Particle Source

Food Water phantom

Pheromone Importance

Analogies with our problem:

Electron beams

Implementation of the algorithm in simulations

First step:

•The entire geometry is divided into

virtual cells.

•The simulation starts with no use of

VRTs.

•The ratio of particles that passing

through every cell, reach the ROI is

registered during the simulation.

•Importance I in each cell is defined as

a function of that ratio (Importance

map).

Electron beams

Implementation of the algorithm in simulations

Second step:

•Once the importance map has

enough information, VRTs can be used.

•Each time a particle arrives to a new

cell, VRTs are applied according to the

particle weight w and the cell’s

importance I.

•If I increases Splitting in w ∙ I particles with w'= I -1.

Electron beams

Implementation of the algorithm in simulations

•If I increases Splitting in w ∙ I particles with w'= I -1.

•If I decreases Russian roulette with probability of

survival w ∙ I. If it survives, w'= I -1.

Electron beams

Implementation of the algorithm in simulations

•If I increases Splitting in w ∙ I particles with w'= I -1.

•If I decreases Russian roulette with probability of

survival w ∙ I. If it survives, w'= I -1.

•Defining I=2 k, with k as integer, all particles in the same

cell have the same weight.

Electron beams

Implementation of the algorithm in simulations

Electron beams

Importance map

( , , , , )I I x y z E m=

Virtual cubic cells of

side 1 cm.

Two values for energy.

Two values for the

material.

E > 6 MeVE < 6 MeV

Air

Dense

mat.

Electron beams

Importance map

When there is few information on

the map, the usefulness of the

algorithm is reduced.

( 1, , , 1, 1)

100

I I x y z E m

N

= = = =

=

Electron beams

Importance map

When there is few information on

the map, the usefulness of the

algorithm is reduced.

( 1, , , 1, 1)

1,000

I I x y z E m

N

= = = =

=

Electron beams

Importance map

When there is few information on

the map, the usefulness of the

algorithm is reduced.

( 1, , , 1, 1)

10,000

I I x y z E m

N

= = = =

=

Electron beams

Importance map

When there is few information on

the map, the usefulness of the

algorithm is reduced.

( 1, , , 1, 1)

500,000

I I x y z E m

N

= = = =

=

Electron beams

Results applying the optimization algorithm

Time simulation is reduced from 220 h to 4.4 h.

Efficiency x 50.

Electron beams

The optimization algorithm allows the

efficient and automatic use of variance

reduction techniques.

Tested on a particular problem.

But is this algorithm general

enough?

Photon beams for radiosurgery

They are very narrow beams used for treatment of small

lesions near healthy structures that has to be preserved.

The characterization of these beams is very complex due

to their small size.

Monte Carlo simulations can be used as a complementary

tool to experimental measurements.

Again, the simulation time can be huge.

Photon beams for radiosurgery

Characterization of the beams

Circular fields generated by a Varian

accelerator 2100C with conical

collimators.

Characterization for the treatment

planner:

•Depth dose distributions and lateral

profiles in water phantom.

•Output factors for each cone.

Photon beams for radiosurgery

Characterization of the beams

•Tuning of the electron beam

incident on a target for

reproducing experimental

measurements.

•We need to apply the

optimization algorithm to

both electrons and photons.

Target

Conical

collimator

Chamber

Flattening Filter

Mirror

Jaws

Primary

collimator

e-

Photon beams for radiosurgery

Application of the optimization algorithm

Importance maps:

1

2

( , , , , )

( , , , , , , )

I I x y z E M

I I x y z E M

=

=

for electrons.

for photons.

Using new variance reduction techniques with photons:

•Russian roulette and splitting No gain in efficiency.

•Directional bremsstrahlung splitting.

Photon beams for radiosurgery

Directional bremsstrahlung splitting

Electrons

Photons

Whenever an event that produces

photons occurs, the event is repeated

w ∙NBr times.

Russian roulette is applied on each

generated photon according to w' ∙ I .

It is used throughout the geometry

and when photons are scattered.

Target

Photon beams for radiosurgery

Left: map for high energy photons pointed to the

phantom. Right: High energy electrons. Brighter

colors correspond to higher importance.

Photon beams for radiosurgery

Simulation Time

Computer Intel Quad

Core Harpertown

E5405 (2.0 GHz).

Version 2008 of

PENELOPE.

Uncertainty 2% (k = 2):

•Cone 10 mm: 9 h.

•Cone 20 mm: 3.6 h.

•Cone 30 mm: 0.9 h.

Conclusions

We have developed an optimization algorithm based on

ant colonies that allows the efficient implementation of

variance reduction techniques in different situations.

It makes use of information registered on importance

maps.

Minimum intervention by the user is required.

Other applications

In addition to the former situations, the optimization

algorithm has been applied in solving other problems:

•Calculation of specific absorbed doses

to organs by nuclear medicine

procedures. Efficiency ×10.

•Computation of correction factors of

micro-ionization chambers.

Efficiency ×100.

•Application of the optimization algorithm to other problems that use the Monte Carlo simulation of radiation transport.

•Implementation in other simulation codes.

•To increase the degree of automation.

•Study of applications of the information stored in the importance maps.

Perspectives

1. García-Pareja S, Vilches M, Lallena AM. Ant colony method to control variance reduction techniques in the Monte Carlo simulation of clinical electron linear accelerators. Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors

and Associated Equipment. 2007;580(1 Spec. Iss.):510-3.

2. Carvajal MA, García-Pareja S, Guirado D, et al. Monte Carlo simulation using the PENELOPE code with an ant colony algorithm to study MOSFET detectors. Physics in Medicine and Biology. 2009;54(20):6263-76.

3. García-Pareja S, Vilches M, Lallena AM. Ant colony method to control variance reduction techniques in the Monte Carlo simulation of clinical electron linear accelerators of use in cancer therapy. Journal of Computational and Applied Mathematics. 2010;233(6):1534-41.

4. García-Pareja S, Galán P, Manzano F, et al. Ant colony algorithm implementation in electron and photon Monte Carlo transport: Application to the commissioning of radiosurgery photon beams. Medical Physics. 2010;37(7):3782-90.

5. Cenizo E, García-Pareja S, Galán P, et al. A jaw calibration method to provide a homogeneous dose distribution in the matching region when using a monoisocentric beam split technique. Medical Physics. 2011;38(5):2374-81.

6. Díaz-Londoño G, García-Pareja S, Salvat F, et al. Monte Carlo calculation of specific absorbed fractions: Variance reduction techniques. Physics in Medicine and Biology. 2015;60(7):2625-44.

Papers